Why protons and neutrons have spins?

In summary: GraberIn summary, the spin quantum numbers of 1/2 and -1/2 can be explained in terms of quarks as the result of two up quarks and one down quark (uud) making up the proton, which is a baryon. The spin value of each quark is 1/2, but due to the complex nature of quantum mechanics, the overall spin of the proton is not simply the sum of the individual spin values. Instead, it involves Clebsch-Gordan coefficients and other intricate algebraic calculations. This phenomenon is still being studied and fully understood in the field of quantum mechanics.
  • #1
Winga
21
0
Their spin quantum numbers are 1/2 and -1/2.

How to explain these in terms of quarks?
 
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  • #2
Because they are made of two up quarks and one down quark (uud), protons are baryons. So are neutrons (udd). The magnitude of the spin-value of each quark is 1/2

marlon
 
  • #3
Composing 3 spins of 1/2,according to Clebsch-Gordan's theorem,doesn't necessarily yield a spin 1/2 state...In fact,it yields a linear combination of 1/2 & 3/2 states.Something more is needed to explain the spin of those 2 barions.

Daniel.
 
  • #4
Angular momentum doesn't add linearly. That is, a proton contains three quarks, but its spin is not 3/2, but 1/2. When you add angular momentum, you have a range of possible results, which goes from the maximum (the arithmetic sum) down to the minimum (the larger minus the smaller) with possible values at unit steps in between. If you add two spin-1/2 fermions, you get either spin 0 or spin 1 (a boson). If you add 5 units of angular momentum to 2 units, you get 3, 4, 5, 6, or 7 units of angular momentum. If you add 3/2 units and 2 units, you get 1/2, 3/2, 5/2, or 7/2 units. A proton has spin 1/2. As you should expect, there's another particle with the same quark content as the proton, but spin 3/2, the Δ+.

marlon
 
  • #5
Are quarks also have spins, +1/2 & -1/2?
 
  • #6
Eigenvalues of [tex] \hat{S}_{z} [/tex]...?Of course.

Daniel.
 
  • #7
Let me just say that the truth is far more complex than the simple constituent quark model could let one think

see for instance : Present understanding of the nucleon spin structure

there are several contribution to the spin of the nucleon, and it is a superbe illustration of the strength of QFT that they precisely add up to exactly one-half. The experimetal resolution of this puzzle is currently being performed.
 
  • #8
Is there any easier way to explain this phenomenon?
 
  • #9
Winga said:
Is there any easier way to explain this phenomenon?

No, sorry, this is QM. Though the explanation by Humanino is entirely correct, i suggest you make sure you understand how addition of the J-operator and the associated Clebsch-Gordan coefficients work. This is basic QM-stuff.

Question is : did you study any QM yet ?

regards
marlon
 
  • #10
Mmmm...not yet!
 
  • #11
Winga said:
Mmmm...not yet!

In that case, Houston we have a problem...


Within what context do you need to answer this question of proton-spin ?


regards
marlon
 
  • #12
No offense,but "Their spin quantum numbers are 1/2 and -1/2.

How to explain these in terms of quarks?" and "Not yet" when asked about studying QM,do not really match.There's an order to everything...You can ask about everything,it's a forum,but the explanations you asked for "...in terms of quarks" are not simple to understand,if you have no theoretical preparation...

Daniel.
 
  • #14
The first site given by astronuc indeed gives a splendid explanation as to why there are six quarks. However, it does not explain the problem at hand here. one cannot bypass the QM-nature of it's solution.

regards
marlon
 
  • #15
marlon said:
Because they are made of two up quarks and one down quark (uud), protons are baryons. So are neutrons (udd). The magnitude of the spin-value of each quark is 1/2

marlon
For protons, the spin of one up quark cancels out the spin of one down quark, and one up quark left with spin value 1/2?
 
  • #16
Unfortunately its not that simple. Spins don't add like regular numbers in quantum mechanics much less field theory. You have to play an intricate game with things called Clebsch Gordon Coefficients and the like. A first course in QM should suffice to explain the correct algebra.
 
  • #17
Would the correct algebra be able to be taught here? If not, where can I find an easy explination of what to do?
 
  • #18
The CRC Handbook for 2002 says:

Winga said:
Their spin quantum numbers are 1/2 and -1/2.

How to explain these in terms of quarks?
Hi Winga,
The free neutron undergoes, with half-life of 614 seconds, a convulsive transformation to a proton + a 782 KeV beta- and its spin is +1/2 and its magnetic dipole moment is -1.913 nuclear magneton units.
The residual Proton's spin is also +1/2 but its magnetic dipole moment is
+2.793 nuclear magniton units. Cheers, Jim
 

Related to Why protons and neutrons have spins?

1. Why do protons and neutrons have spins?

The spin of a particle is an intrinsic property that cannot be explained by classical physics. Protons and neutrons, as fundamental particles, have a spin of 1/2, which is a quantum mechanical property. This spin is necessary to explain the magnetic properties of these particles.

2. How is the spin of a proton or neutron determined?

The spin of a particle is determined experimentally through scattering experiments. These experiments involve firing particles at high speeds and measuring their interactions. The results of these experiments have shown that protons and neutrons have a spin of 1/2.

3. Is the spin of a proton or neutron always the same?

Yes, the spin of a proton or neutron is a fundamental property that does not change. However, the direction of the spin can vary, resulting in different spin states for a particle. This is known as spin angular momentum and is also a quantum mechanical property.

4. How does the spin of a proton or neutron relate to its magnetic moment?

The spin of a particle is directly related to its magnetic moment. The magnetic moment is a measure of the strength of a particle's magnetic field. For protons and neutrons, their spin is the primary contributor to their magnetic moment, making them behave like tiny magnets.

5. Are there any other particles with a spin of 1/2?

Yes, the spin of 1/2 is a common property among fundamental particles. In addition to protons and neutrons, electrons, muons, and neutrinos also have a spin of 1/2. This spin is a fundamental aspect of the Standard Model of particle physics and is essential in understanding the interactions between particles.

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